1. **State the problem:** We need to find the equation of a line with slope $m=1$ that passes through the point $(-2,5)$. The equation should be in slope-intercept form $y=mx+b$. 2. **Recall the slope-intercept form:** The general form is $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Use the point-slope form to find $b$:** Substitute $m=1$, $x=-2$, and $y=5$ into the equation: $$5 = 1 \times (-2) + b$$ 4. **Simplify and solve for $b$:** $$5 = -2 + b$$ Add 2 to both sides: $$5 + 2 = b$$ $$b = 7$$ 5. **Write the final equation:** $$y = 1x + 7$$ Or simply: $$y = x + 7$$ This is the equation of the line in slope-intercept form.